The following points highlight the top four elements of cost of capital. The elements are:- 1. Cost of Equity Capital (K_{e}) 2. Cost of Retained Earnings (K) 3. Cost of Preferred Capital (Kp) 4. Cost of Debt (Kd).

**Element # 1. Cost of Equity Capital (K**_{e}):

_{e}):

The funds required for the project are raised from the equity shareholders, which are of permanent nature. These funds need not be repayable during the life time of the organization. Hence it is a permanent source of funds. The equity shareholders are considered to be the owners of the company.

The main objective of the firm is to maximize the wealth of the equity shareholders. Equity share capital is the risk capital of the company. If the company’s business is doing well the ultimate beneficiaries are the equity shareholders who will get the return in the form of dividends from the company and the capital appreciation for their investment.

If the company comes for liquidation due to losses, the ultimate and worst sufferers are the equity shareholders. Sometimes they may not get their investment back during the liquidation process.

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Profits after taxation, less preference dividends paid out to the preference shareholders, are funds that belong to the equity shareholders which are reinvested in the company and therefore, those retained funds should be included in the category of equity, the cost of retained earnings is discussed separately from cost of equity capital.

The cost of equity may be defined as the minimum rate of return that a company must earn on the equity share capital financed portion of an investment project so that market price of the shares remain unchanged. The following methods are used in calculation of cost of equity.

**Dividend Yield Method****:**

The dividend per share is expected on the current market price per share. As per this method, the cost of capital is defined as **“the discount rate that equates the present value of all expected future dividends per share with the net proceeds of the sale (or the current market price) of a share.”**

This method is based on the assumption that the market value of equity shares is directly related to the future dividends on those shares. Another assumption is that the future dividend per equity share is expected to be constant and the company is expected to earn at least this yield to keep the equity shareholders content.

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K_{e} = D_{1}/P_{0}

Where,

K_{e} = Cost of equity capital

D_{1} = Annual dividend per share on equity capital in period 1

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P_{0} = Current market price of equity share

This method emphasizes on future equity dividend expected to be constant. It does not allow for any growth rate. But in reality, a shareholder expects the returns from his equity investment to grow over time. This approach has no relevance to the company.

**Illustration 1****:**

Radiant Ltd. is expected to disburse a dividend of Rs. 30 on each equity share of Rs. 10. The current market price of share is Rs. 80. Calculate the cost of equity capital as per dividend yield method.

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**Solution**:

Rs. 30

K_{e }= Rs.30/Rs.30 = 0.375 or 37.5%

**Illustration 2****:**

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Fox Ltd. issued 10,000 equity shares of Rs. 10 each at a premium of Rs. 2 each. The company has incurred issue expenses of Rs. 5,000. The equity shareholders expects the rate of dividend to 18% p.a. Calculate the cost of equity share capital. Will your answer be different if the current market price of share is Rs. 21?

**Solution**:

**Since the equity shares are newly issued, the cost of capital of it can be calculated as follows: **

K_{e }= D_{1}/NP

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Where,

D_{1} = Expected dividend per equity share of current year

NP = Net proceeds of each equity share

Net proceeds = (10,000 Equity shares x Rs. 12) – Rs. 5,000/10,000 Equity shares = Rs. 11.50 per share

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K_{e} = 1.80/11.50 = 0.1565 or 15.65%

**In case of existing equity shares, market price is to be taken as basis for calculation of cost of equity capital as follows: **

Where, D, = Expected dividend pc equity share of current year i.e. Rs. 1.80

P_{0} = Current market price per equity share i.e. Rs. 21

K_{e} = 1.80/21 = 0.0857 or 8.57%

**Dividend Growth Model****:**

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Equity shareholders will normally expect dividend to increase year after year and not to remain constant in perpetuity. In this method, an allowance for future growth in dividend is added to the current dividend yield. It is recognized that the current market price of a share reflects expected future dividends. This model is also called as ‘Gordon growth model’.

K_{e} = D_{1}/P_{0} + g

Where,

D_{1} = Expected dividend per equity share

P_{0} = Current market price per equity share

g = Growth rate by which dividends are expected to grow per year at a constant compound rate

**Criticism: **

**The dividend growth model is criticized on the following reasons: **

(a) The future growth pattern is impossible to predict because it will be inconsistent and uneven.

(b) Due to uncertainty of future and imperfect information, only historic growth is to be used for prediction of future growth.

(c) Calculation of only cost of equity capital, ignoring the cost of other forms of capital, may not be valid.

(d) The dividend growth depends on the retained earnings of the company and the growth is difficult to assume.

**Illustration 3****:**

The equity of Mercury Ltd. are traded in the market at Rs. 90 each. The expected current year dividend per share is Rs. 18. The subsequent growth in dividends is expected at the rate of 6%. Calculate the cost of equity capital.

**Solution****:**

K_{e} = D_{e}/P_{0 }+ g = 18/90 + 0.06 = 0.20 + 0.06 = 0.26 or 26%

**Illustration 4****:**

Sun Ltd. has its shares of Rs. 10 each quoted on the stock exchange, the current price per share is Rs. 24. The gross dividends per share over the last four years have been Rs. 1.20, Rs. 1.32, Rs. 1.45 and Rs. 1.60. Calculate the cost of equity shares.

**Solution****:**

Expected current year dividend

= Rs.1.60 x 110/100 = Rs. 1.76

The dividends are growing @ 10% and are expected to continue to grow at this rate.

K_{e} = 1.76/24 + 0.10 = 0.07 + 0.10 = 0.17 or 17%

**Illustration 5****:**

**The details of dividend paid by Cool Ltd. on its existing equity shares of Rs. 10 each for the past 6 years is given below: **

The current market price of equity shares is Rs. 40. It is expected to maintain the fixed dividend payout ratio in the future. The company has issued new equity shares of Rs. 10 each and the cost of its flotation is Re. 0.50 per share. The expected dividend to be declared for the current year is Rs. 1.40. Using the above information calculate the cost of equity capital.

**Solution: **

During the last 5 years (Year 2004 is ignored since the dividend of 2004 is compared with the dividend of 2009), the dividend has increased from Rs. 1.05 to Rs. 1.34.

Compound factor = Rs. 1.34/Rs. 1.05 = 1.2762

By looking into compound value of Re. 1 (compound table given at the end of the book) the sum of Re. 1 would accumulate to Rs. 1.2762 in five years is 5%. Therefore, the dividend growth rate is 5%.

K_{e} = D_{1}/NP+g

D_{1} = Expected dividend of current year (2005) i.e., Rs. 1.40

NP = Net proceeds i.e., Rs. 10 – Re. 0.50 = Rs. 9.50 g

G = 5% or 0.05

K_{e} = 1.40/9.50 + 0.05 = 0.1474 + 0.05 = 0.1974 or 19.74%

**Sometimes the dividend growth model formula for calculation of cost of equity share capital is also written as follows, if last declared dividend is known: **

K_{e} = D_{o} (1 + g)/P_{0 }+ g

Where,

D_{o} = Recent dividend paid per equity share

g = Constant annual growth rate of dividends

P_{0} = Current dividend market price per share

**Illustration 6****:**

Bright Star Ltd. has its equity shares of Rs. 10 each quoted in a stock exchange has market price of Rs. 56. A constant expected annual growth rate of 6%, and a dividend of Rs. 3.60 per share has been paid for the current year. Calculate the cost of capital.

**Solution**:

K_{e} = D_{o} (1+g)/P_{0}+g

= 3.60(1+0.06)/56+0.06 = 0.0681+0.06 = 0.1281 or 12.81%

**Price Earning Method****:**

This method takes into consideration the earnings per share (EPS) and the market price of the share. It is based on the assumption that the investors capitalise the stream of future earnings of the share and the earnings of a share need not be in the form of dividend and also it need not be disbursed to the shareholders.

It is based on the argument that even if the earnings are not disbursed as dividends, it is kept in the retained earnings and it causes future growth in the earnings of the company as well as the increase in market price of the share. In calculation of cost of equity share capital, the earnings per share is divided by the current market price.

K_{e }= E/M

Where, E = Current earnings per share

M = Market price per share

**Illustration 7****:**

Prabhat Ltd. has 50,000 equity shares of Rs. 10 each and its current market value is Rs. 45 each. The after tax profit of the company for the year ended 31st March, 2009 is Rs. 9,60,000. Calculate the cost of capital based on price/earning method.

**Solution: **

EPS = Rs. 9,60,000/50,000 equity shares = Rs. 19.20

K_{e }= E/M = 19.20/45 = 0.4267 or 42.67%

**Capital Asset Pricing Model****:**

The capital asset pricing model (CAPM) divides the cost of equity into two components, the near risk-free return available on investing in government bonds and an additional risk premium for investing in a particular share or investment. This risk premium in turn comprises the average return on the overall market portfolio and the beta factor (risk factor) of the particular investment.

**Putting this all together the CAPM assesses the cost of equity for an investment as the following: **

R_{i} = Risk-free rate of return

R_{m} = Average market return

β_{i} = Beta of the investment

The appropriate discount rate to apply to the forecasted cashflows in an investment appraisal is the opportunity cost of capital for that investment. The opportunity cost of capital is the expected rate of return offered in the capital markets for investments of a similar risk profile. Thus it depends on the risk attached to the investment’s cashflows.

**Illustration 8****:**

Modern Ltd.’s share beta factor is 1.40. The risk free rate of interest on government securities is 9%. The expected rate of return on company equity shares is 16%. Calculate cost of equity capital based on capital asset pricing model.

**Solution**:

K. = 9% + 1.40 (16% – 9%) = 9%+1.40 (7%) = 18.8%

**Element # 2. ****Cost of Retained Earnings (K)****:**

The retained earnings is one of the major sources of finance available for the established companies to finance its expansion and diversification programs. These are the funds accumulated over years of the company by keeping a part of the funds generated without distribution. The retained earnings are a pool of funds so generated becomes one of the major source of funding for the company to its expansion and diversification programs.

So long as the retained profits are not distributed to the shareholders, the company can use the funds within the company for further profitable investment opportunities. The equity shareholders of the company are entitled to these funds and these funds should also be taken into account while calculating the cost of equity capital.

Some argue that retained earnings are cost free funds available with the company, on which no return is payable. The retained earnings are the distributable profits available for equity shareholders, kept with the company without distributing them in the form of dividends. If the retained earnings are distributed among equity shareholders, the amount would have been reinvested to earn return on it.

Therefore, the cost of retained earnings may be considered equivalent to the return forgone by the equity shareholders and it is the opportunity cost of funds not available for reinvestment by the individual shareholders. In other words, the retained earnings has the cost equivalent to opportunity rate of earnings forgone by the equity shareholders.

Hence cost of equity includes retained earnings. But in practice, retained earnings are a slightly cheaper source of capital as compared to the cost of equity capital. Therefore, the cost of retained earnings is treated separately from the cost of equity capital.

**Opportunity Cost Approach****:**

The cost of retained earnings to the shareholders is basically an opportunity cost of such funds to them. It is equal to the income that they would otherwise obtain by placing these funds in alternative investment. The cost of retained earnings is determined based on the opportunity rate of earnings of equity shareholders which is being forgone continuously.

**If the retained earnings are distributed to the equity shareholders attract personal taxation of the individual shareholders and therefore, the cost of earnings is calculated as follows: **

K_{r} = D (1 – T_{i}) Where,

K_{r} = Cost of retained earnings

D = Dividend rate

T_{i} = Tax rate of individuals

**Illustration 26.9****:**

The dividend paid on equity share capital of Spectrum Ltd. is 24%. The personal taxation of individual shareholders is 35%. Calculate the cost of retained earnings.

**Solution****:**

K = 24% (1 – 0.35) = 15.6%

**Rights Offer Approach: **

Retaining of profits within the organization will add on to the net-worth of the company and it results in increase of price rise in equity shares. According to rights offer approach, the shareholder is entitled for profits retained.

Suppose if the company distributed the retained profits in the form of dividends to the equity holders and again call-back the money through rights offer, the dividends paid to the individual shareholder attract personal taxation and the shareholders are in a position to subscribe for rights offer only to the extent of net dividends received from the company.

If the retained earnings are kept within the company, the price of shares will raise to the extent of retained profits which will attract capital gains tax on the individual shareholder. Therefore, it will not change the position of the shareholder whether the retained profits are distributed among shareholders as dividends or kept it with the company. The following formula is used for calculation of cost of retained earnings, under rights offer approach.

K_{r} = D (1 -T_{i}) /P (1 – T_{c})

Where,

K_{r} = Cost of retained earnings

D = Dividend rate

T_{i}= Marginal tax rate on income of individual shareholder

T_{c} = Capital gains tax

P = Market price per share

**Illustration 10****:**

Danlaw Ltd. has paid an equity dividend of Rs. 3 per share. The market price of its equity share is Rs. 25. The marginal tax rate being at 40% and capital gains tax being at 30%. Calculate the cost of retained earnings under rights offer approach.

**Solution****:**

Where the equity shareholders have no tax liability, then the following formula is used for

K_{r} = D/P

In practice, cost of retained earnings is taken to be the same as market rate of capitalization, due to difficulty in ascertainment of tax rate of individual equity shareholders.

**Element # 3. ****Cost of Preferred Capital (K**_{p})**:**

_{p})

The cost of preference share capital is the rate of return that must be earned on preference capital financed investments, to keep unchanged the earnings available to the equity shareholders.

**Cost of Irredeemable Preference Shares****:**

The cost of irredeemable preference share capital is the rate of preference dividend, also called the coupon rate divided by net issue proceeds.

K_{p} = D_{p}/NP

**Where,**:

K_{p} = Cost of irredeemable preference shares

D_{p} = Preference dividend

NP = Net proceeds received from issue of preference shares after meeting the issue expenses.

**Illustration 11****:**

Green Fields Ltd. has issued 10,00,000 irredeemable preference shares of Rs. 150 each at a coupon rate of 14% p.a. The issue expenses are Rs. 15 per share. Calculate the cost of preference share capital.

**Solution****:**

K_{p }= 21/135 = 0.1555 or 15.55%

**Cost of Redeemable Preference Shares****:**

**The cost of redeemable preference shares is calculated as follows: **

Where,

K_{p} = Cost of preference shares

D = Constant annual preference dividend payment

N = Number of years to redemption

Rv = Redeemable value of preference shares at the time of redemption

Sv = Sale value of preference shares less discount and flotation expenses

**Illustration 12****:**

Dell Ltd. has Rs. 100 preference share redeemable at a premium of 10% with 15 years maturity. The coupon rate is 12%. Flotation cost is 5%. Sale price is Rs. 95. Calculate the cost of preference shares.

**Solution****:**

**Element # 4. ****Cost of Debt (K**_{d})**:**

_{d})

The capital structure of a firm normally includes the debt component also. Debt may be in the form of debentures, bonds, term loans from financial institutions and banks etc.

The debt is carried a fixed rate of interest payable to them, irrespective of the profitability of the company. Since the coupon rate is fixed, the firm increases its earnings through debt financing. Then, after payment of fixed interest charges more surplus is available for equity shareholders, and hence EPS will increase.

An important point to be remembered that dividends payable to equity shareholders and preference shareholders is an appropriation of profit, whereas the interest payable on debt is a charge against profit.

Therefore, any payment towards interest will reduce the profit and ultimately the company’s tax liability would decrease. This phenomenon is called ‘tax shield’. The tax shield is viewed as a benefit accrues to the company which is geared.

**To gain the full tax shield, the following conditions apply: **

(i) The company must be able to show a taxable profit every year to take full advantage of the tax shield.

(ii) If the company makes loss, the tax shield goes down and cost of borrowing increases.

**Illustration 13: **

**Harper Ltd. has earned a profit before interest and tax of Rs. 6,00,000 for the year ended 31st March, 2009. Calculate its profit after tax in the following situations: **

(i) The project has entirely financed through issue of 3,00,000 equity shares of Rs. 10 each.

(ii) The company has financed its project through issue of 1,00,000 equity shares of Rs. 10 each and 20,000, 14% debentures of Rs. 100 each.

The company’s applicable corporate tax rate is 40%.

**Solution****:**

By using the tax shield and advantage of fixed interest bearing funds in the capital structure, the EPS of the owners i.e. equity shareholders is increased by Re. 0.72 (i.e., Rs. 1.92 – Rs. 1.20)

In a situation of loss making the advantage of tax shield and gearing cannot be gained. It will further increase the cost of debt.

**The debt may be perpetual debt or redeemable debt and for calculation of cost of debt the following information is required: **

(a) Net cash inflow from each source of debt and cost of raising debt.

(b) The amount of periodic interest payment and principal repayment on maturity.

(c) Corporate taxation rate.

**Nominal and Real Cost of Debt: **

The real cost of debt will be less than the nominal cost as investors are not compensated for the real drop in value of their funds. Thus the real of cost of debt is lesser than the cost of debt calculated in the above formulae. The calculation of real cost of debt is explained in the following illustration.

**Illustration 14**:

M Ltd. has issued 14% Debentures and the inflation rate was 5%.

**The real cost of the loan can be calculated by using the following formula:**

Real cost of debt = Nominal cost of debt/ Inflation rate = 1.14/1.05 = 1.086 = 8.6%

**Cost of Perpetual Debt****:**

**The cost of redeemable debt is calculated by applying the following formula:**

K_{d} = I(1-t)/NP

Where, K_{d }= Cost of debt

I = Annual interest payment

t = Company’s effective corporate tax rate

NP = Net proceeds of issue of debentures, bonds, term loans etc.

**Illustration 15:**

Vishnu Steels Ltd. has issued 30,000 irredeemable 14% debentures of Rs. 150 each. The cost of flotation of debentures is 5% of the total issued amount. The company’s taxation rate is 40%. Calculate the cost of debt.

**Solution**:

**Cost of Redeemable Debt:**

**The cost of redeemable debt is calculated by applying the following formula:**

Where

K_{d} = Cost of debt

I = Annual interest payment

RV = Redeemable value of debt at the time of maturity

SV = Sale value less discount and flotation expenses

N = Number of years to maturity

t = Company’s effective tax rate

**Illustration**** 16**:

Surya Industries Ltd. has raised funds through issue of 10,000 debentures of Rs. 150 each at a discount of Rs. 10 per debenture with 10 years maturity. The coupon rate is 16%. The flotation cost is Rs. 5 per debenture. The debentures are redeemable with a 10% premium. The corporate taxation rate is 40%. Calculate the cost of debentures.

**Solution****:**

If the debt raised is certain of its redemption at the end of specified period, the cost of debt capital can be calculated on the internal rate of return (IRR) basis.

**Illustration 17****:**

Business Machines Ltd. has issued redeemable debentures of Rs. 100 each repayable at the end of 8 year period on a coupon rate of 14%. The flotation expenses is 10% of issue amount. Calculate the cost of debt.

**Cost of Deep Discount Bonds and Zero Coupon Bonds****:**

Sometimes, bonds are issued at large discount and no interest is payable on them during their tenure of life. At the time of redemption, the nominal value of the bond will be repaid to the bond holders.

**Calculation of cost of debt on these deep discount bonds is illustrated below: **

**Illustration**** 18: **

Express Cargo Ltd. has issued 5 years zero coupon bonds of Rs. 1,000 each at a price of Rs.540. calculate the cost of debt.

**Cost of Convertible Debentures****:**

**The calculation of cost of fixed interest debentures which are convertible into equity shares is explained in the following illustration: **

**Illustration 19****:**

Searock Ltd. has issued 14% convertible debentures of Rs. 100 each at par. Each debenture will be convertible into 8 equity shares of Rs. 10 each at a premium of Rs. 5 per share. The conversion will take place at the end of 4 years. The corporate tax rate is assumed to be 40%. Assume that tax savings occur in the same year that the interest payments arise. The flotation cost is 5% of the issue amount. Calculate the cost of convertible debentures.

**Solution****:**

**Cost of Floating Debt****:**

Now the companies are raising debt on a rate of interest that varies from time to time. In floating debt rate, a certain percentage of interest will be of fixed nature over and above the fixed rate of interest, the lender will charge extra rate of interest depending on the money market and economic policies of the country.

The commercial banks are now lending at prime lending rate plus variable portion of interest that vary from customer to customer. The variable portion will act like a risk premium. In case of established and financially sound companies the variable rate will be lesser and in case risk is attached to the lending the variable rate will be more.

An example for floating debt rate is if a company raises from external sources on terms of LIBOR + 3%. The company will be paying a rate of interest on its loan equal to whatever rate LIBOR is, plus an extra 3%. (This 3% is the fixed margin or spread). And so, if LIBOR is 6%, the company pays 9% interest on its loan; if LIBOR falls to 5%, the company’s loan interest rate will fall to 8%.

**Illustration 20****:**

N Ltd. has raised a term loan of Rs. 2 crores from a commercial bank on a prime lending rate plus 4%. The prime lending rate of the bank is 12%. The company’s corporate rate of tax is 40%. Calculate the cost of debt raised from the bank.

**Solution**:

**The company pays a rate of interest to the bank is: **

= 12% + 4% = 16%

K_{d} = 16% (1 – 0.40) = 9.6%